SUN Yan, ZHOU Gang, LIU Zheng-xing. Plane Infinite Analytical Element and Hamiltonian System[J]. Applied Mathematics and Mechanics, 2003, 24(5): 505-511.
Citation: SUN Yan, ZHOU Gang, LIU Zheng-xing. Plane Infinite Analytical Element and Hamiltonian System[J]. Applied Mathematics and Mechanics, 2003, 24(5): 505-511.

Plane Infinite Analytical Element and Hamiltonian System

  • Received Date: 2001-02-10
  • Rev Recd Date: 2002-12-24
  • Publish Date: 2003-05-15
  • It is not convenient to solve those engineering problems defined in an infinite field by using FEM.An infinite area can be divided into a regular infinite external area and a finite internal area.The finite internal area was dealt with by the FEM and the regular infinite external area was settled in a polar coordinate.All governing equations were transformed into the Hamiltonian system.The methods of variable separation and eigenfunction expansion were used to derive the stiffness matrix of a new infinite analytical element.This new element,like a super finite element,can be combined with commonly used finite elements.The proposed method was verified by numerical case studies.The results show that the preparation work is very simple,the infinite analytical element has a high precision,and it can be used conveniently.The method can also be easily extended to a three-dimensional problem.
  • loading
  • [1]
    徐芝纶.弹性力学[M].北京:高等教育出版社,1990.
    [2]
    Timoshenko S P,Goodier J N.Theory of Elasticity[M].3rd Ed.New York:McGraw-Hill,1970.
    [3]
    Sokolnikoff I S.Mathematical Theory of Elasticity[M].2nd Ed.New York:McGraw-Hill,1956.
    [4]
    Zienkiewiz O C,Taylor R W.The Finite Element Method[M].Vol 2.4th Ed.New York:McGraw-Hill,1989.
    [5]
    应隆安.无限元方法[M].北京:北京大学出版社,1992.
    [6]
    ZHONG Wan-xie,Williams F W.Physical interpretation of the symplectic orthogonality of the eigensolutions of a Hamiltonian or symplectic matrix[J].Computers & Structures,1993,49(4):749-750.
    [7]
    ZHONG Wan-xie.LIN Jia-hao.QIU Chun-hang.The eigenvalue problem of the chain of identical substructures[J].Acta Mechanica Sinica,1991,7(2):169-177.
    [8]
    钟万勰.弹性平面扇形域问题及哈密顿体系[J].应用数学和力学,1994,15(12):1057-1066.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2156) PDF downloads(559) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return